Bioassay Problem Research Articles

Simultaneous Confidence Intervals for Ratios of Fixed Effect Parameters in Linear Mixed Models

In multiple comparisons of fixed effect parameters in linear mixed models, treatment effects can be reported as relative changes or ratios. Simultaneous confidence intervals for such ratios had been previously proposed based on Bonferroni adjustments or multivariate normal quantiles accounting for the correlation among the multiple contrasts. We propose Fieller-type intervals using multivariate t quantiles and the application of Markov chain Monte Carlo techniques to sample from the joint posterior distribution and construct percentile-based simultaneous intervals. The methods are compared in a simulation study including bioassay problems with random intercepts and slopes, repeated measurements designs, and multicenter clinical trials.

A note on comparison and improvement of estimators based on likelihood

The problem of estimation of a parameter of interest in the presence of a nuisance parameter, which is either location or scale, is considered. Three estimators are taken into account: usual maximum likelihood (ML) estimator, maximum integrated likelihood estimator and the bias-corrected ML estimator. General results on comparison of these estimators w.r.t. the second-order risk based on the mean-squared error are obtained. Possible improvements of basic estimators via the notion of admissibility and methodology given in Ghosh and Sinha [A necessary and sufficient condition for second order admissibility with applications to Berkson's bioassay problem. Ann Stat. 1981;9(6):1334–1338] are considered. In the recent paper by Tanaka et al. [On improved estimation of a gamma shape parameter. Statistics. 2014; doi:10.1080/02331888.2014.915842], this problem was considered for estimating the shape parameter of gamma distribution. Here, we perform more accurate comparison of estimators for this case as well as for some other cases.

Consistency and asymptotic normality of the estimated effective doses in bioassay

In order to estimate the effective dose such as the 0.5 quantile ED 50 in a bioassay problem various parametric and semiparametric models have been used in the literature. If the true dose–response curve deviates significantly from the model, the estimates will generally be inconsistent. One strategy is to analyze the data making only a minimal assumption on the model, namely, that the dose–response curve is non-decreasing. In the present paper we first define an empirical dose–response curve based on the estimated response probabilities by using the “pool-adjacent-violators” (PAV) algorithm, then estimate effective doses ED 100 p for a large range of p by taking inverse of this empirical dose–response curve. The consistency and asymptotic distribution of these estimated effective doses are obtained. The asymptotic results can be extended to the estimated effective doses proposed by Glasbey [1987. Tolerance-distribution-free analyses of quantal dose–response data. Appl. Statist. 36 (3), 251–259] and Schmoyer [1984. Sigmoidally constrained maximum likelihood estimation in quantal bioassay. J. Amer. Statist. Assoc. 79, 448–453] under the additional assumption that the dose–response curve is symmetric or sigmoidal. We give some simulations on constructing confidence intervals using different methods.

Tumour Incidence, Prevalence and Lethality Estimation in the Absence of Cause-of-Death Information

Summary A Bayesian intensity model is presented for studying a bioassay problem involving interval-censored tumour onset times, and without discretization of times of death. Both tumour lethality and base-line hazard rates are estimated in the absence of cause-of-death information. Markov chain Monte Carlo methods are used in the numerical estimation, and sophisticated group updating algorithms are applied to achieve reasonable convergence properties. This method was tried on the rat tumorigenicity data that have previously been analysed by Ahn, Moon and Kodell, and our results seem to be more realistic.

Forecasting the Penetration of a New Product—A Bayesian Approach

We adopt a Bayesian approach to forecast the penetration of a new product into a market. We incorporate prior information from an existing product and/or management judgments into the data analysis. The penetration curve is assumed to be a nondecreasing function of time and may be under shape constraints. Markov-chain Monte Carlo methods are proposed and used to compute the Bayesian forecasts. An example on forecasting the penetration of color television using the information from black-and-white television is provided. The models considered can also be used to address the general bioassay and reliability stress-testing problems.

Analyzing Ultimatum Bargaining: A Bayesian Approach to the Comparison of Two Potency Curves Under Shape Constraints

An experiment designed to test whether experimenter observation influences play of the ultimatum game led to a comparison of proportions of perfect equilibria obtained under different conditions. Our analysis features a Bayesian approach to this comparison. Our method extends recent work in the nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve. Sampling-based approaches to calculating posterior features of interest are used and discussed. We conclude that experimenter observation has a small influence but not enough to account for most of the deviation from perfect-equilibrium play.

Further investigations of berkson's example

Berkson's bioassay problem is investigated in detail. In addition to maximum likelihood estimators and Berkson's proposed minimum logit χ2 estimators, several modified estimators are considered. Two Rao-Blackwellized estimators - a conditional mean and conditional median, given the sufficient statistics - as well as Amemiya's bias-corrected and partially bias-correct estimators are included. The estimators are compared with respect to bias, variance, mean squared error, and Pitman's measure of closeness. The experiment is examined at four different levels of the parameters, and is re-examined subject to a monotonicity condition imposed on the sample space. The results provide a new insight into the controversy over the comparison of minimum χ2 and maximum likelihood estimators.

Nonparametric Bayesian bioassay with prior constraints on the shape of the potency curve

SUMMARY We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

An example arising from berkson's conjecture

Berkson (1980) conjectured that minimum x2 was a superior procedure to that of maximum likelihood, especially with regard to mean squared error. To explore his conjecture, we analyze his (1955) bioassay problem related to logistic regression. We consider not only the criterion of mean squared error for the comparison of these estimators, but also include alternative criteria such as concentration functions and Pitman's measure of closeness. The choice of these latter criteria is motivated by Rao's (1981) considerations of the shortcomings of mean squared error. We also include several Rao-Blackwellized versions of the minimum logit x2 the purpose of these comparisons.

Small-Sample Confidence Limits for Parameters under Inequality Constraints with Application to Quantal Bioassay

A family of methods is presented for constructing confidence limits for the parameters of a collection of distributions when a simple ordering is assumed among the parameters. The methods are shown to yield confidence limits that are exact or conservative for finite samples. For discrete distributions, one of the methods produces confidence limits that are at least as tight as the limits produced by a commonly used single-sample procedure. Confidence limits are demonstrated for a binomial quantal bioassay problem assuming a nondecreasing dose-response function. Results of a simulation study show that competing asymptotic methods can produce serious discrepancies between nominal and actual coverage probabilities for binomial samples of sizes up to 30, and demonstrate that the new approach can be competitive with the asymptotic methods when the latter maintain their nominal error rates.

Linear Bayes estimators of the potency curve in bioassay

Abstract : The Bayesian nonparametric approach to estimating the tolerance distribution in quantal bioassay has received some attention. The computational difficulty in evaluating these Bayes estimators has hindered their applications. This paper explores the linear Bayes approach to the bioassay problem. These linear Bayes estimators can be computed easily by using statistical software which has the capability of inverting a matrix. Let us state the quantal bioassay problem as follows: The experimenter intends to test the potency of a stimulus by giving subjects injections of the stimulus at different levels; namely, he chooses L dosage levels, t sub 1,...., t sub L, and treats n sub 1,....,n sub L subjects at these levels respectively. Each subject possesses a fixed tolerance level. If a stimulus exceeds a subject's tolerance level, the subject responds positively. If not, there is no response. Therefore we observe the number of positive responses at each level. These numbers are denoted by k sub 1,...,k sub l. The potency curve F is the distribution of tolerance levels; i.e. F is defined by the probability F(t) of getting a positive response to a dosage at level t for all t. The objective of this article is to make inferences about the potency curve F. Keywords: Ferguson's Dirichlet process.

Weighted averaging of species indicator values: Its efficiency in environmental calibration

A common bioassay problem in applied ecology is to estimate values of an environmental variable from species incidence or abundance data. An example is the problem of reconstructing past changes in acidity (pH) in lakes from diatom assemblages found in successive strata of the bottom sediment. The method of weighted averaging is based on indicator values, the indicator value of a species being, intuitively, the value of the environmental variable most preferred by that species. Indicator values of all species present in a site are averaged to give an estimate of the value of the environmental variable at the site. The average is weighted by species abundances, if known, with absent species having zero weight. Using field data, several authors have compiled lists of indicator values of species for various environmental variables for use in weighted averaging, e.g. pH indicator values of diatom species. In this paper the properties of the method of weighted averaging are studied, starting from the idea that indicator values are parameters of response curves that describe the expected abundance of each species in relation to the environmental variable. In practice the response curves must be estimated by regression methods, but here they are assumed to be known in advance. Conditions are derived under which the weighted average is a consistent and efficient estimator for the value of an environmental variable at a site. Because weighted averaging is central to the ordination technique known as reciprocal averaging or correspondence analysis, the conditions also define models that are implicitly invoked when reciprocal averaging is used in ecological ordination studies.

The antiprogestin RU38 486: receptor-mediated progestin versus antiprogestin actions screened in estrogen-insensitive T47Dco human breast cancer cells.

Despite the theoretical promise of synthetic antiprogestational agents as anticancer agents, experimental tools, midcycle contraceptives, and implantation inhibitors, none has been available for either basic or clinical studies. However, a candidate antiprogestin, RU38 486 [17 beta-hydroxy-11 beta-(4-dimethylaminophenyl)17 alpha-(1-propynl)estra-4,9 -dien-3-one], has recently been described that has antiprogestational and antiglucocorticoid activities in early clinical trials. Its mechanisms of action are unclear. Furthermore, development of this drug underscores an old bioassay problem: that biological screening of progestins and antiprogestins is complex because of the physiological requirement that progestational effects must be superimposed upon an estrogenized system. This has made it difficult to distinguish among progestational, antiprogestational, and antiestrogenic properties of unknown agents. Here we describe the use of T47Dco human breast cancer cells to circumvent these problems. T47Dco cells are rich in progesterone receptors (PR), but are resistant to estrogens and antiestrogens. Their PR are estrogen-independent, and this permits progestins to be studied in an estrogen-free system. We have used these cells to assess the receptor-binding properties and the biological actions of RU38 486. Since RU38 486 absorbs UV at approximately 300 nm, this wavelength was used to covalently photolink the drug to PR in situ. Like the synthetic progestin R5020, low concentrations (10 nM) of [3H]RU38 486 bind two PR subunits in nuclei of T47Dco; glucocorticoid receptors are not bound. RU38 486 has a high affinity for PR in vitro (Kd approximately 2 nM at 0-4 C), and in intact cells, low concentrations (6-8 nM) transform more than 95% of PR to a high affinity nuclear binding state. In contrast to progesterone, the compound is not metabolized, so that it chronically (3-6 days) suppresses PR replenishment. These biochemical properties of RU38 486 are typical of synthetic progestins, but distinguish it from pure glucocorticoids. To bioassay RU38 486, we have measured growth and insulin receptors, since in T47Dco, physiological concentrations of progestins inhibit proliferation and increase the number of cell surface insulin-binding sites. Like progestins, RU38 486 is growth inhibitory; unlike progestins, it fails to stimulate insulin receptors and partially blocks their stimulation by R5020. Thus, RU38 486 has dual progestin agonist/antagonist actions depending on the biological response measured.

Review and evaluation of the NCI/NTP carcinogenesis bioassays.

A comparison of the carcinogenesis bioassay results obtained by the National Cancer Institute (NCI) and the National Toxicology Program (NTP) indicates that approximately one-half of the bioassays directed by both institutions were positive for carcinogenicity. The more recent 85 bioassays completed by NTP reveal a higher proportion of studies interpreted as demonstrating no evidence of carcinogenicity than represented in the initial 198 bioassays conducted by NCI. Of the 100 NCI bioassays that were not positive for carcinogenicity 3 (3%) were classified in the category of "no evidence for carcinogenicity in two animal species." Of the 43 NTP bioassays that were not positive for carcinogenicity 36 (84%) were placed in the category of "no carcinogenic effects." The reason for this shift from a 33:1 positive to negative ratio in the NCI bioassays to an approximately 1:1 ratio in the NTP bioassays appears to be a difference in interpretation of the adequacy of the testing. For example, 6 of the 36 NTP negative bioassays involved testing in only one species. Uniform criteria for concluding that a bioassay is negative must be developed and the results of all existing and future carcinogenesis bioassays must be interpreted with these exclusive criteria. Other bioassay problems are explored, including the incomplete validation of the carcinogenesis bioassay protocol by confirmatory results with positive and negative reference agents, the apparent lack of bioavailability data for some orally administered negative compounds, the continued use of mouse hepatic neoplasia as a single discriminating parameter, the variability in the inter- and intrastudy incidence of spontaneous tumors, and the continued reliance on the maximum tolerated dose.

The science of teratology in a regulatory setting.

The science of teratology is discussed from a regulatory point of view. A brief history of this branch of toxicology is presented with emphasis on specific instances of the inadvertent production of birth defects in humans as a result of exposure to exogenous agents. The basic principles of teratology are elucidated as a means of understanding current test protocols and their scientific rationale. A typical, general protocol is given and some of the major shortcomings of such a bioassay are presented. Among these shortcomings are the problems of significance of fetal toxicity and lack of a postnatal component to the teratology test system. The teratogenic and/or fetotoxic potential of selected pesticides are examined with special reference to the bioassay problems alluded to. Pesticides discussed include cacodylic acid, endrin, benomyl, ETU, nitrofen, and mirex. Finally, a brief discussion of a proposed teratology screen using pregnant laboratory animals is presented.

On the convolution of logistic random variables

An expression is obtained for the distribution of a convolution of independent and identically distributed logistic random variables by directly inverting the characteristic function. This distribution is shown to be closely approximated by a student'st distribution when both distribution are standardized. Moreover, by showing that some of the analytic simplicity and statistical properties that are manifest in the single logistic also obtain in the convolution, an application of the convolution as a dose-response curve in the bio-assay problem is suggested.

A Necessary and Sufficient Condition for Second Order Admissibility with Applications to Berkson's Bioassay Problem

A theorem is proved which gives a necessary and sufficient condition for improving, up to $o(n^{-2})$, the mean squared error of the maximum likelihood estimate $\hat{\theta}$ by using an estimate of the form $\hat{\theta} + d(\hat{\theta})/n$. An application is made to a bioassay problem of Berkson.

Robust estimators for quantal bioassay

SUMMARY Extensions of robust estimators for the location of a symmetric distribution are given for the quantal bioassay problem. Asymptotic properties of the estimators are derived. A comparison in terms of asymptotic efficiencies under different tolerance distributions is made between the Spearman-Karber estimator and the trimmed mean and Tukey biweight estimators.

The application of stochastic approximation methods to the bio-assay problem

A new general model for the bio-assay problem is introduced. It is shown that when the slope of the dose-response curve and the median effective dose is known, the Robbins-Monro method yields an asymptotically optimal estimation procedure. Adaptive procedures are discussed for the case of unknown slope. Results of Monte Carlo studies are given.

Some properties of Spearman-type estimators of the variance and percentiles in bioassay

Theoretical results for the Spearman-type variance estimator in the quantal response bioassay problem are determined when the mean of the underlying tolerance distribution is known, and also when it is unknown. For an experiment with infinitely many dose levels, the estimator is proved to be finite with probability one, and its mean and variance are given. Allowing the dose interval to approach zero, the estimator is shown to be asymptotically normal and asymptotically highly efficient. Similar asymptotic findings are also reached for a Spearman-type percentile estimator. The results approximate the performance of Spearman-type estimators in most practical situations and argue for their use.